Hollow Sections in Structural Applications 2nd Edition

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HOLLOW SECTIONS IN

STRUCTURAL APPLICATIONS

J. Wardenier, J.A. Packer, X.-L. Zhao and G.J. van der Vegte


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ISBN 978-90-72830-86-9

CIDECT, Geneva, Switzerland, 2010

The publisher and authors have made careful efforts to ensure the reliability of the data contained in thispublication, but they assume no liability with respect to the use for any application of the material and

information contained in this publication.

Printed by Bouwen met Staal

Boerhaavelaan 402713 HX Zoetermeer, The Netherlands

P.O. Box 1902700 AD Zoetermeer, The Netherlands

Tel. +31(0)79 353 1277

Fax +31(0)79 353 1278E-mail [email protected]

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PREFACE

The global construction market requires a world-wide coordination of product-, testing-, design- and execution-standards, so that contracts for delivery of products and for engineering- and construction services can beagreed on a common basis without barriers.

The mission of CIDECT is to combine the research resources of major hollow section manufacturers in order tocreate a major force in the research and application of hollow steel sections world wide. This forms the basis ofestablishing coordinated and consistent international standards.

For the ease of use of such standards, it is however necessary to reduce their content to generic rules and toleave more object-oriented detailed rules to accompanying non-conflicting complementary information, thathave the advantage to be more flexible for the adaptation to recent research results and to be useable togetherwith any international code.

The book by J. Wardenier, J.A. Packer, X.-L. Zhao and G.J. van der Vegte "Hollow sections in structural

applications" is such a source, developed in an international consensus of knowledge on the topic. Itincorporates the recently revised design recommendations for hollow sections joints of the InternationalInstitute of Welding, IIW (2009) and CIDECT (2008 and 2009). Both are consistent with each other and are thebasis for the Draft ISO standard for Hollow Section Joints (ISO 14346) and may form the basis for futuremaintenance, further harmonisation and further development of Eurocode 3 (EN 1993-1-8), AISC (ANSI/AISC360) and the CISC recommendations.

For the use together with EN 1993-1-8 and ANSI/AISC 360, both being based on the previous IIW (1989)recommendations, the main differences to these rules are highlighted.

The authors are all internationally recognized experts in the field of tubular steel structures, three of themhaving been chairmen of the IIW-Subcommission XV-E on "Tubular Structures" since 1981. This committee is

the pre-eminent international authority producing design recommendations and standards for onshore tubularstructures.

This book should therefore be an invaluable resource for lecturers, graduate students in structural, architecturaland civil engineering, explaining the important principles in the behaviour of tubular steel structures. It is alsoaddressed to designers of steel structures who can find in it the special items related to the use of hollowsections, in particular joints, their failure modes and analytical models as supplements to more general designcodes.

Aachen, Germany, August 2010

Prof. Dr.-Ing. Dr.h.c. Gerhard Sedlacek

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ACKNOWLEDGEMENTS

This book gives the background to design with structural hollow sections in general and in particular for joints tohollow sections. For the latter, the recently updated recommendations of the International Institute of Welding(IIW, 2009) and CIDECT (2008 and 2009) are adopted.

The background to design recommendations with the relevant analytical models is especially important forstudents in Structural and Civil Engineering, whereas the design recommendations themselves serve more asan example. Since the available hours for teaching Steel Structures, and particularly Tubular Structures, varyfrom country to country, this book has been written in a modular form. The presentation generally followsEuropean codes, but the material is readily adapted to other (national) codes.

Since the first edition of this book was used not only by students but also by many designers, this secondedition was needed due to the recent update of the recommendations by IIW and the subsequent revision ofthe CIDECT Design Guides Nos. 1 and 3 in 2008 and 2009.

The new IIW (2009) recommendations and the revised CIDECT Design Guides Nos. 1 and 3 (2008 and 2009)are consistent with each other and are the basis for the Draft ISO standard for Hollow Section Joints (ISO14346). Although the current Eurocode 3 (EN 1993-1-8, 2005) and AISC (2010) recommendations are stillbased on the previous IIW (1989) and CIDECT (1991 and 1992) recommendations, it is expected that in thenext revision these will follow the new IIW and CIDECT recommendations presented in this book.

Besides the static design recommendations and background for hollow section joints, information is given formember design in Chapter 2, composite structures in Chapter 4, and fire resistance in Chapter 5. Thesechapters fully comply with the latest versions of the Eurocodes (EN 1993 and EN 1994). Further, fatigue designof hollow section joints is covered in Chapter 14.

We wish to thank our colleagues from the IIW Sub-commission XV-E "Tubular Structures" and from the

CIDECT Project Working Group and the CIDECT Technical Commission for their constructive comments duringthe preparation of this book.

We are very grateful that Prof. J. Stark and Mr. L. Twilt were willing to check Chapters 4 and 5 respectively oncomposite members and fire resistance.

Appreciation is further extended to the authors of CIDECT Design Guides Nos. 1 to 9 and to CIDECT formaking parts of these Design Guides or background information available for this book.

Finally, we wish to thank CIDECT for the initiative to update this book.

Delft, The Netherlands, September 2010

Jaap WardenierJeffrey A. PackerXiao-Ling ZhaoAddie van der Vegte


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CONTENTS

1. Introduction 11.1 History and developments 11.2 Designation 21.3 Manufacturing of hollow sections 2

2. Properties of hollow sections 92.1 Mechanical properties 92.2 Structural hollow section dimensions and dimensional tolerances 102.3 Geometric properties 112.4 Drag coefficients 142.5 Corrosion protection 142.6 Use of internal void 152.7 Aesthetics 15

3. Applications 293.1 Buildings and halls 293.2 Bridges 293.3 Barriers 293.4 Offshore structures 303.5 Towers and masts 303.6 Special applications 30

4. Composite structures 374.1 Introduction 374.2 Design methods 374.3 Axially loaded columns 37

4.4 Resistance of a section to bending 394.5 Resistance of a section to bending and compression 394.6 Influence of shear forces 394.7 Resistance of a member to bending and compression 394.8 Load introduction 414.9 Special composite members with hollow sections 41

5. Fire resistance of hollow section columns 495.1 Introduction 495.2 Fire resistance 505.3 Unfilled hollow section columns 525.4 Concrete filled hollow section columns 53

5.5 Water filled hollow section columns 555.6 Joints 56

6. Design of hollow section trusses 656.1 Truss configurations 656.2 Joint configurations 656.3 Limit states and limitations on materials 666.4 General design considerations 676.5 Truss analysis 68

7. Behaviour of joints 757.1 General introduction 757.2 General failure criteria 777.3 General failure modes 77

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7.4 Joint parameters 77

8. Welded joints between circular hollow sections 818.1 Introduction 818.2 Modes of failure 818.3 Analytical models 81

8.4 Experimental and numerical verification 838.5 Basic joint strength formulae 838.6 Evaluation to design rules 848.7 Other types of joints 858.8 Design charts 868.9 Relation to the previous recommendations of IIW (1989) and CIDECT (1991) 878.10 Concluding remarks 87

9. Welded joints between rectangular hollow sections 1039.1 Introduction 1039.2 Modes of failure 103

9.3 Analytical models 1049.4 Experimental and numerical verification 1069.5 Basic joint strength formulae 1069.6 Evaluation to design rules 1079.7 Other types of joints or other load conditions 1079.8 Design charts 1099.9 Concluding remarks 109

10. Welded joints between hollow sections and open sections 12910.1 Introduction 12910.2 Modes of failure 12910.3 Analytical models 129

10.4 Experimental verification 13110.5 Evaluation to design rules 13110.6 Joints predominantly loaded by bending moments 131

11. Welded overlap joints 14111.1 Introduction 14111.2 Modes of failure 14111.3 Analytical models for RHS overlap joints 14111.4 Analytical models for CHS overlap joints 14311.5 Analytical models for overlap joints with an open section chord 14311.6 Experimental and numerical verification 14311.7 Joint strength formulae 144

12. Welded I beam-to-CHS or RHS column moment joints 15112.1 Introduction 15112.2 Modes of failure 15112.3 Analytical models 15112.4 Experimental and numerical verification 15312.5 Basic joint strength formulae 15312.6 Concluding remarks 154

13. Bolted joints 16113.1 Flange plate joints 16113.2 End joints 161

13.3 Gusset plate joints 16213.4 Splice joints 162

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13.5 Beam-to-column joints 16213.6 Bracket joints 16313.7 Bolted subassemblies 16313.8 Purlin joints 16313.9 Blind bolting systems 16313.10 Nailed joints 163

14. Fatigue behaviour of hollow section joints 17514.1 Definitions 17514.2 Influencing factors 17514.3 Loading effects 17614.4 Fatigue strength 17714.5 Partial factors 17714.6 Fatigue capacity of welded joints 17714.7 Fatigue capacity of bolted joints 17914.8 Fatigue design 180

15. Design examples 19315.1 Uniplanar truss of circular hollow sections 19315.2 Uniplanar truss of square hollow sections 19715.3 Multiplanar truss (triangular girder) 19715.4 Multiplanar truss of square hollow sections 19915.5 Joint check using the joint resistance formulae 19915.6 Concrete filled column with reinforcement 200

16. References 209

Symbols 221

CIDECT 229


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1. INTRODUCTION

Design is an interactive process between thefunctional and architectural requirements and thestrength and fabrication aspects. In a good design, all

these aspects have to be considered in a balancedway. Due to the special features of hollow sectionsand their joints, it is here even of more importancethan for steel structures of open sections. Thedesigner should therefore be aware of the variousaspects of hollow sections.

Many examples in nature show the excellentproperties of the tubular shape with regard to loadingin compression, torsion and bending in all directions,see Figs. 1.1 and 1.2. These excellent properties arecombined with an attractive shape for architectural

applications (Figs. 1.3 and 1.4). Furthermore, theclosed shape without sharp corners reduces the areato be protected and extends the corrosion protectionlife (Fig. 1.5).

Another aspect which is especially favourable forcircular hollow sections is the lower drag coefficients ifexposed to wind or water forces. The internal void canbe used in various ways, e.g. to increase the bearingresistance by filling with concrete or to provide fireprotection. In addition, heating or ventilation systemssometimes make use of the hollow section columns.

Although the manufacturing costs of hollow sectionsare higher than those for other sections, leading tohigher unit material cost, economical applications areachieved in many fields. The application field coversall areas, e.g. architectural, civil, offshore, mechanical,chemical, aeronautical, transport, agriculture andother special fields. Although this book will be mainlyfocused on the background to design and application,in a good design not only does the strength have to beconsidered, but also many other aspects, such asmaterial selection, fabrication including welding and

inspection, protection, erection, in service inspectionand maintenance.

One of the constraints initially hampering theapplication of hollow sections was the design of the joints. However, nowadays design recommendationsexist for all basic types of joints, and further researchevidence is available for many special types of joints.

Based on the research programmes carried out,CIDECT (Comit International pour le Dveloppementet l'Etude de la Construction Tubulaire) has publishedDesign Guides Nos. 1 to 9 for use by designers inpractice. Since these nine Design Guides are all

together too voluminous for educational purposes anddo not give the theoretical background, it was decidedto write this book especially to provide backgroundinformation for students and practitioners in Structuraland Civil Engineering.

This book is written in a limit states design format

(also known as LRFD or Load and Resistance Factor

Design in the USA). This means that the effect of the

factored loads (the specified or unfactored loads

multiplied by the appropriate load factors) should not

exceed the factored resistance of the joint or member.

The factored resistance expressions, in general,

already include appropriate material and joint partial

safety factors (M ) or joint resistance (or capacity)

factors (). This has been done to avoid interpretation

errors, since some international structural steelwork

specifications use M

values 1,0 as dividers (e.g.

Eurocodes), whereas others use values 1,0 as

multipliers (e.g. in North America and Australia). In

general, the value of 1/M is almost equal to .

1.1 HISTORY AND DEVELOPMENTS

The excellent properties of the tubular shape havebeen recognised for a long time; i.e. from ancient time,nice examples are known. An outstanding example ofbridge design is the Firth of Forth Bridge in Scotland

(1890) with a free span of 521 m, shown in Fig. 1.6.This bridge has been built up from tubular membersmade of rolled plates which have been rivetedtogether, because at that time, other fabricationmethods were not available for these sizes.

In the same century, the first production methods forseamless and welded circular hollow sections weredeveloped. In 1886, the Mannesmann brothersdeveloped the skew roll piercing process(Schrgwalzverfahren), shown in Fig. 1.7, which madeit possible to roll short thick walled tubulars. This

process, in combination with the pilger process(Pilgerschrittverfahren, Fig. 1.8), developed someyears later, made it possible to manufacture longerthinner walled seamless hollow sections.

In the first part of the previous century, an Englishman,Whitehouse, developed the fire welding of circularhollow sections. However, the production of weldedcircular hollow sections became more important afterthe development of the continuous welding process in1930 by the American, Fretz Moon (Fig. 1.9).Especially after the Second World War, welding

processes have been perfected, which made itpossible for hollow sections to be easily welded

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together.

The end cutting required for fitting two circular hollowsections together was considerably simplified by thedevelopment of a special end preparation machine byMller (Fig. 1.10).

For manufacturers who did not have such end cuttingmachines, the end preparation of circular hollowsections remained a handicap.

A way of avoiding the connection problems was theuse of prefabricated connectors, e.g. in 1937Mengeringhausen developed the Mero system. Thissystem enabled the fabrication of large spacestructures in an industrialized way (Fig. 1.11).

In 1952, the rectangular hollow section was developedby Stewarts and Lloyds (now Corus Tubes). Thissection, with nearly the same properties as thecircular hollow section, enables the connections to bemade by straight end cuttings.

In the fifties, the problems of manufacturing, endpreparation and welding were all solved and from thatpoint of view the way to a successful story was open.The remaining problem was the determination of thestrength of unstiffened joints.

The first preliminary design recommendations fortruss connections between circular hollow sectionswere given by Jamm in 1951. This study was followedby several investigations in the USA (Bouwkamp,1964; Natarajan & Toprac, 1969; Marshall & Toprac,1974), Japan (Togo, 1967; Natarajan & Toprac,1968), and Europe (Wanke, 1966; Brodka, 1968;Wardenier, 1982; Mang & Bucak, 1983; Puthli, 1998;Dutta, 2002).

Research on joints between rectangular hollowsections started in Europe in the sixties, followed by

many other experimental and theoreticalinvestigations. Many of these were sponsored byCIDECT.

Besides these investigations on the static behaviour,in the last 25 years much research was carried out onthe fatigue behaviour and other aspects, such asconcrete filling of hollow sections, fire resistance,corrosion resistance and behaviour under windloading.

1.2 DESIGNATION

The preferred designations for structural applicationsare:- Circular hollow sections (CHS)- Rectangular hollow sections (RHS)- Square hollow sections (SHS)

In Canada and the USA, it is common to speak aboutHollow Structural Sections (HSS), whereas in Europealso the term Structural Hollow Sections (SHS) isused.

1.3 MANUFACTURING OF HOLLOWSECTIONS

As mentioned, hollow sections can be producedseamless or welded. Seamless hollow sections aremade in two phases, i.e. the first phase consists ofpiercing an ingot and the second step considers theelongation of this hollow bloom into a finished circularhollow section. After this process, the tube can gothrough a sizing mill to give it the required diameter.More information about other processes, most of thembased on the same principle, is given by Dutta (2002).

Nowadays, welded hollow sections with a longitudinalweld are mainly made employing either electrical

resistance welding processes or induction weldingprocesses, shown in Fig. 1.12. A strip or plate isformed by rollers into a cylindrical shape and weldedlongitudinally. The edges are heated, e.g. by electricalresistance, then the rollers push the edges together,resulting in a pressure weld. The weld protrusion onthe outside of the tube is trimmed immediately afterwelding.

Rectangular hollow sections are made by deformingcircular hollow sections through forming rollers, asshown in Fig. 1.13. This forming process can be done

hot or cold, using either seamless or longitudinallywelded circular hollow sections. Although it iscommon practice to use longitudinally welded hollowsections, for the very thick sections, seamlesssections may be used.

Square or rectangular hollow sections are sometimesmade by forming a single strip to the required shapeand closing it by a single weld, preferably in themiddle of a face.

Large circular hollow sections are also made by rollingplates through a so-called U-O press process shownin Fig. 1.14. After forming the plates to the required

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shape, the longitudinal weld is made by a submergedarc welding process.

Another process for large tubulars is to use acontinuous wide strip, which is fed into a formingmachine at an angle to form a spirally formed circular

cylinder, see Fig. 1.15. The edges of the strip arewelded together by a submerged arc welding processresulting in a so-called spirally welded tube.

More detailed information about the manufacturingprocesses and the limitations in sizes can be obtainedfrom Dutta (2002).

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Fig. 1.1 Reeds in the wind

Fig. 1.3 Airport Bangkok, Thailand

Fig. 1.2 Bamboo

Fig. 1.4 Ripshorster Bridge, Germany

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Fig. 1.5 Paint surface for hollow sections vs open

sections

Fig. 1.7 Skew roll piercing process(Schrgwalzverfahren)

Fig. 1.6 Firth of Forth Bridge, Scotland

Fig. 1.8 Pilger process (Pilgerschrittverfahren)

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forming rollers

heating

welding rollers welded CHS

heating

coil

forming rollers

heating

welding rollers welded CHS

heating

coil

Fig. 1.9 Fretz Moon process

Fig. 1.11 Mero connector

Fig. 1.10 End cutting machine

Pressure rollers

inductor

Welded CHS

Pressure rollers

inductor

Welded CHS

Pressure rollers

inductor

Welded CHS

Fig. 1.12 Induction welding process

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Fig. 1.13 Manufacturing of rectangular hollow sections

Fig. 1.14 Forming of large CHS

Fig. 1.15 Spirally welded CHS

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2. PROPERTIES OF HOLLOWSECTIONS

2.1 MECHANICAL PROPERTIES

Hollow sections are made of similar steel as used forother steel sections, thus in principle there is nodifference in mechanical properties.

Tables 2.1a and 2.2a show, as an example, themechanical properties according to the Europeanstandard EN 10210-1 (2006) for hot finished structuralhollow sections of non-alloy and fine grain structuralsteels. The cold formed sections are given in EN10219-1 (2006): Cold formed welded structural hollowsections of non-alloy and fine grain structural steels(see Tables 2.1b and 2.2b). As shown, the

requirements of EN 10210-1 and EN 10219-1 arealmost identical.

Hollow sections can also be produced in specialsteels, e.g. high strength steel with yield strengths upto 690 N/mm2 or higher, weathering steels and steelwith improved or special chemical compositions, etc.

Generally, the design of members is based on the

yield strength. In this chapter the recommended M0

andM1 factors of 1,0 are adopted for the design yield

strength fyd

.

In statically indeterminate structures, sufficientdeformation capacity or rotation capacity is requiredfor redistribution of loads. In this case, yielding ofmembers or yielding in the joints may provide therequired rotation capacity. A tensile member made ofductile steel can be brittle if a particular cross sectionis weakened, e.g. by holes, in such a way that thiscross section fails before the whole member yields. Itis therefore required that yielding occurs first. Thisshows that the yield-to-ultimate tensile strength ratio is

also important, especially for structures with verynon-uniform stress distributions, which is a situationthat occurs in tubular joints. Some codes, such asEurocode 3 (EN 1993-1-1, 2005), specify the followingrequirement for the minimum ratios:

1,1f

f

yd

u (2.1a)

The IIW (2009) recommendations and many offshorecodes require a higher ratio between fu and fyd:

8,0f

for25,1

f

f

u

yd

yd

u (2.1b)

This is only one aspect for ductility. In the case ofimpact loading, the steel and members should also

behave in a ductile manner. Hence, Tables 2.1a and2.2a also give requirements based on the standardCharpy test to ensure adequate notch toughness.

Nowadays, more refined characterisation methodsexist to describe the ductility of cracked bodies, e.g.the CTOD (Crack Tip Opening Displacement) method.These characterisation methods are generally usedfor pressure vessels, transport line pipes and offshoreapplications, which are beyond the scope of this book.

Another characterisation is sometimes required for

thick walled sections which are loaded in thethickness direction. In this case, the strength andductility in the thickness direction should be sufficientto avoid cracking, called lamellar tearing, see Fig. 2.1.This type of cracking is caused by non metallicmanganese-sulphide inclusions. Thus, if the sulphurcontent is very low or the sulphur is joined with otherelements such as calcium (Ca), such a failure can beavoided. Indirectly this is obtained by requiring acertain reduction of area RAZ in the tensile test. Forexample, RAZ = 35 means that in the tensile test thecross sectional area at failure has been reduced by

35% compared to the original cross sectional area.

In most structural steel specifications the minimumrequired yield strength, ultimate tensile strength,elongation and the Charpy V-notch values arespecified. Design standards or specifications givefurther limitations for the fu/fy ratio, whereas dependingon the application, more restrictive requirements maybe given related to CTOD values or the properties inthe thickness direction (Z quality).

Another aspect is the effect of cold forming on themechanical properties of the parent steel. In the caseof cold forming of hollow sections, the yield strengthand to a lesser extent the ultimate tensile strength areincreased, especially in the corners, as shown in Fig.2.2. Further, the yield-to-ultimate tensile ratio isincreased and the elongation slightly decreased.

If the standards, e.g. EN 10210-1 and EN 10219-1,specify the properties at a particular cross section

location based on the finished product, these

properties have been already partly taken into

account. Thus, this generally applies in Europe.

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However, some standards outside Europe specify thematerial properties of the parent material. In this case,the increased yield strength can be taken into accountfor design. A small corner radius produces a smallcold formed area with a large cold forming effect andconsequently a large increase in yield strength, while

a large corner radius does just the opposite.According to research work of Lind & Shroff (1971),the product of area and increase in yield strength canapproximately be taken as constant. Lind & Shroffassumed that in every corner of 90 the yield strengthof the parent material fyb is increased over a length of7t to the ultimate tensile strength of the parentmaterial fu. The total increase over the section 4(7t)t(fu-fyb) can be averaged over the section, resulting in adesign yield strength fya, as shown in Fig. 2.2.

It is noted that the cold formed sections should satisfythe requirements for minimum inside corner radius toguarantee sufficient ductility, see Table 2.3 for fullyaluminum killed steel (steel with limited Si content).

Part 10 of Eurocode 3 (EN 1993-1-10, 2005) specifies

the material selection. Here, a permissible thickness

can be determined based on a reference temperature,

the steel grade and quality and the stress level. The

reference temperature covers, besides the air

temperature, also cold forming effects, strain rate, etc.

However, the current rules cannot be adopted to cold

formed hollow sections because the determination ofthe effect of cold forming for cold formed hollow

sections is not yet clearly specified. Based on the data

obtained by Soininen (1996), Kosteski et al. (2003),

Bjrk (2005), Khn (2005), Puthli & Herion (2005) and

Sedlacek et al. (2008), presently a proposal is being

worked out for an amendment of EN 1993-1-10. In

this proposal of CEN/TC 250/SC 3-N 1729 (2010), it is

recommended that for cold formed hollow sections

according to EN 10219, the procedure for hot formed

material can be used provided that for the cold

forming effects the reference temperature is reduced

by Tcf. For CHS, Tcf varies from 0 C to 20 C

depending on the thickness and the d/t ratio. For RHS

with steel qualities according to EN 10219, Tcfvaries

from 35C to 45C depending on the thickness and

the ratio between the inside corner radius and the

thickness. For cold formed hollow sections with

Charpy impact strengths significantly exceeding the

requirements of EN 10219, a lower value of Tcf is

allowed.

2.2 STRUCTURAL HOLLOW SECTIONDIMENSIONS AND DIMENSIONALTOLERANCES

The dimensions and sectional properties of structural

hollow sections have been standardised in EN (EN10210-2, 2006; EN 10219-2, 2006) and ISO standards(ISO 657-14, 2000; ISO 4019, 2001) for hot finishedand cold formed structural hollow sectionsrespectively.

The two applicable standards in Europe are EN10210-2 (2006) "Hot finished structural hollowsections of non-alloy and fine grain steels Part 2:Tolerances, dimensions and sectional properties" andEN 10219-2 (2006) "Cold formed welded structuralhollow sections of non-alloy and fine grain steels

Part 2: Tolerances, dimensions and sectionalproperties". However, the majority of manufacturers ofstructural hollow sections do not produce all the sizesshown in these standards. It should be further notedthat other sizes, not included in these standards, maybe produced by some manufacturers.

The majority of the tolerances given in EN 10219-2are the same as those in EN 10210-2, see Tables2.4a and 2.4b.

Internationally, the delivery standards in various

countries deviate considerably with respect to thethickness and mass tolerances (Packer, 1993). Inmost countries besides the thickness tolerance, amass tolerance is given, which limits extremedeviations. However, in some production standards,e.g. in the USA, the thickness tolerance is not alwayscompensated by a mass tolerance. This has resultedin associated design specifications which account forthis, by designating a lower "design wall thickness" of0,9 or 0,93 times the nominal thickness t. In Eurocode3, where design is based on nominal thicknesses, thethickness tolerances in EN 10210-2 and EN 10219-2are (partly) compensated by the mass tolerance. It isforeseen that in the next revision these tolerances willbe tightened.

Although the circular, square and rectangular hollowsections are the generally-used shapes; other shapesare sometimes available. For example, some tubemanufacturers deliver the shapes given in Table 2.5.Of these, the elliptical hollow sections have becomemore popular for architectural designs. These shapesare not dealt with further in this book. However, more

information about elliptical hollow sections can befound in Bortolotti et al. (2003), Chan & Gardner(2008), Choo et al. (2003), Martinez-Saucedo et al.

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(2008), Packer et al. (2009b), Pietrapertosa & Jaspart(2003), Theofanous et al. (2009), Willibald et al.(2006) and Zhao & Packer (2009).

2.3 GEOMETRIC PROPERTIES

2.3.1 Tension

The design capacity Nt,Rd of a member under tensileloading depends on the cross sectional area and thedesign yield strength, and is independent of thesectional shape. In principle, there is no advantage ordisadvantage in using hollow sections from the pointof view of the amount of material required. The designcapacity is given by:

ydRd,tAfN (2.2)

If the cross section is weakened by bolt holes or slots,the net cross section should also be checked, in asimilar way as for other sections, e.g. according toEurocode 3 (EN 1993-1-8, 2005):

9,0fA

N2M

unetRd,t

(2.3)

where the partial safety factorM2 = 1,25.

The factor 0,9 may vary from country to countrydepending on the partial factorM used. Where ductilebehaviour is required (e.g. under seismic loading), theyield resistance shall be less than the ultimateresistance at the net section of fastener holes.

2.3.2 Compression

For centrally loaded members in compression, thecritical buckling load depends on the slenderness

and the section shape.

The slenderness is given by the ratio of the bucklinglength b and the radius of gyration i.

ib (2.4)

The radius of gyration of a hollow section (in relationto the member mass) is generally much higher thanthat for the weak axis of an open section. For a givenlength, this difference results in a lower slenderness

for hollow sections and thus a lower mass whencompared with open sections.

The buckling behaviour is influenced by initialeccentricities, straightness and geometrical tolerancesas well as residual stresses, non-homogeneity of thesteel and the stress-strain relationship.

Based on extensive investigations by the European

Convention for Constructional Steelwork (ECCS) andCIDECT, "European buckling curves" (Fig. 2.3 andTable 2.7) have been established for various steelsections including hollow sections. They areincorporated in Eurocode 3 (EN 1993-1-1, 2005).

The reduction factor shown in Fig. 2.3 is the ratio ofthe design buckling capacity Nb,Rd to the axial plasticcapacity.

yd

Rd,b

Rd,pl

Rd,b

f

f

N

N (2.5)

where:

fb,Rd =A

N Rd,b (2.6)

The non-dimensional slenderness is determinedby:

E

(2.7)

where:

yE f

E (Euler slenderness) (2.8)

The buckling curves for the hollow sections areclassified according to Table 2.6. Most open sectionsfall under curves "b" and "c". Consequently, for thecase of buckling, the use of hot formed hollowsections generally provides a considerable saving inmaterial.

Fig. 2.4 illustrates, for a buckling length of 3 m, acomparison between the required mass of open andhollow sections for a given load. It shows that in thosecases in which loads are small, leading to relativelyslender sections, hollow sections provide a greatadvantage (considerably lower use of material).However, if loads are higher, resulting in lowslenderness, the advantage (in %) will be less.

The overall buckling behaviour of hollow sectionsimproves with increasing diameter- or width-to-wall

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thickness ratio. However, this improvement is limitedby local buckling. To prevent local buckling, d/t or b/tlimits are given e.g. in Eurocode 3 (EN 1993-1-1,2005), see Table 2.7. In the case of thin walledsections, interaction between global and local bucklingshould be considered.

In addition to the improved buckling behaviour due tothe high radius of gyration and the enhanced designbuckling curve, hollow sections can offer otheradvantages in lattice girders. Due to the torsional andbending stiffness of the members in combination with joint stiffness, the effective buckling length ofcompression members in lattice girders can bereduced (Fig. 2.5). Eurocode 3 (EN 1993-1-1)recommends an effective buckling length for hollowsection brace members in welded lattice girders equalto or less than 0,75, in which represents the systemlength, see also Rondal et al. (1992).

For chords, 0,9 times the system length for in-planebuckling or 0,9 times the length between the supportsfor out-of-plane buckling, is taken as the effectivebuckling length.

These reductions are also based on the fact that thechord and brace members are generally not fullyoptimised. If for example the chord would be fullyutilized with different members for every panel then

these reductions would not be allowed.

Laterally unsupported compression chords of latticegirders (see Fig. 2.6) have a reduced buckling lengthdue to the improved torsional and bending stiffness ofthe tubular members (Baar, 1968; Mouty, 1981).These factors make the use of hollow sections ingirders or trusses even more favourable.

2.3.3 Bending

In general, I and H sections are more economicalunder bending about the major axis (Imax larger thanfor hollow sections). Only in those cases in which thedesign resistance in open sections is largely reducedby lateral buckling, hollow sections offer anadvantage.

It can be shown by calculations that lateral instabilityis not critical for circular hollow sections, squarehollow sections and for the most commonly usedrectangular hollow sections with bending about thestrong axis. Table 2.8 shows allowable span-to-depth

ratios for the most commonly used sections (EN1993-1-1, 2005). According to a study of Kaim (2006)

these limits can be taken considerably larger.

It is apparent that hollow sections are especiallyfavourable compared to other sections if bendingabout both axes is present.

Hollow sections used for elements subjected tobending can be more economically designed by usingplastic design. However, then the sections have tosatisfy more restricted conditions to avoid prematurelocal buckling. Like other steel sections loaded inbending, different moment-rotation behaviour can beobserved.

Fig. 2.7 shows various moment-rotation diagrams fora member loaded by bending moments.

The moment-rotation curve "1" shows a momentexceeding the plastic moment Mpl and a considerablerotation capacity. Moment-rotation curve "2" shows amoment exceeding the plastic moment capacity Mpl,but after the maximum, the moment dropsimmediately, so that little moment-rotation capacityexists. Moment-rotation curve "3" represents acapacity lower than the plastic moment capacity,which, however, exceeds the yield moment capacityMel. In the moment-rotation curve "4" the capacity iseven lower than the yield moment capacity Mel andfailure is by elastic buckling. The effect of the

moment-rotation behaviour is reflected in theclassification of cross sections as shown in Fig. 2.8and Table 2.7. The cross section classification isgiven in limits for the diameter- or flatwidth-to-thickness ratio.

The limits are based on experiments and can beexpressed as:

ydf

235c

t

d for CHS (2.9)

f

235c3

t

b

yd

for RHS (2.10a)

ydf

235c3

t

h for RHS (2.10b)

with fyd in N/mm2 and c depending on the section

class, the cross section and the loading. For RHS, it isconservatively assumed that the width of the "flat" isequal to the external width b or depth h of the RHS

minus 3t.

12


21/240

The cross section classes 1 and 2 can develop theplastic moment capacity up to the given b/t or d/t limitswith bi-linear stress blocks, whereas the momentcapacity of the cross section classes 3 and 4 is basedon an elastic stress distribution (see Fig. 2.8). Thedifference between the cross section classes 1 and 2

is reflected in the rotation capacity. After reaching theplastic moment capacity, the cross section class 1 cankeep this capacity after further rotation, whereas thecapacity of the cross section class 2 drops afterreaching this capacity. As a consequence, themoment distribution in the structure or structuralcomponent should be determined by elastic analysisfor structures made of sections with cross sectionclasses 2, 3 or 4. For structures made of sections withcross sections in class 1 a plastic moment distributioncan be adopted, but an elastic moment distribution isstill permissible (and in some countries morecommon).

For a class 1 beam fully clamped at both ends andsubjected to a uniformly distributed loading q, theplastic moment distribution implies that after reachingthe plastic moment capacity at the ends, the beamcan be loaded until a further plastic hinge occurs atmid span (see Fig. 2.9).

For the class 4 cross section, the maximum stress isdetermined by local buckling and the stress in the

outer fibre is lower than the yield strength fy.Alternatively, an effective cross sectional area basedon the yield strength may be determined.

Detailed information about the cross sectionalclassification is given by Rondal et al. (1992).

Research by Wilkinson & Hancock (1998) showed

that especially the limits for the side wall slenderness

of RHS need to be reduced considerably. E.g. for

class 1 sections, they suggest reducing the Eurocode

3 limits (EN 1993-1-1) for the side wall slenderness to:

6t

)2r2t5(b70

t

2r)2t(h

(2.11)

with 30t

r2t2b

For r = t, this can be simplified to:

t

b83,077

t

h with 34

t

b (2.11a)

In the absence of shear forces or if the shear forces

do not exceed 50% of the shear capacity Vpl,Rd, theeffect of shear may be neglected and the bendingmoment capacity about one axis is given by:

ydplRd,c fWM for cross section classes 1 or 2 (2.12)

ydelRd,c fWM for cross section class 3 (2.13)

ydeffRd,c fWM for cross section class 4 (2.14)

When the shear force exceeds 50% of the shearcapacity, combined loading has to be considered, seeEurocode 3 (EN 1993-1-1).

2.3.4 Shear

The elastic shear stress in circular and rectangularhollow sections can be determined with simplemechanics by:

3

f

tI2

SV yd

Ed (2.15)

Fig. 2.10 shows the elastic stress distribution. Thedesign capacity based on plastic design can be easilydetermined based on the Huber-Hencky-Von Misescriterion by assuming the shear yield strength in those

parts of the cross section active for shear.

3

fAV ydvRd,pl (2.16)

where:

hb

hAA v

for RHS (2.17)

(or just 2ht) with V in the direction of h.

A2

A v

for CHS (2.18)

2.3.5 Torsion

Hollow sections, especially CHS, have the mosteffective cross section for resisting torsional moments,because the material is uniformly distributed about thepolar axis. A comparison of open and hollow sections

of nearly identical mass in Table 2.9 shows that thetorsional constant of hollow sections is about 200times that of open sections.

13


22/240

The design capacity for torsional moments isdescribed by:

3

fWM ydtRd,t (2.19)

or circular hollow sections:F

t)td(2td

I2W tt

(2.20)

here:w

ttd4

I 3t

(2.21)

or rectangular hollow sections (Marshall, 1971):F

A

m

tt A

2t

IW

(2.22)

here:w

A

A3

t

tA4

3

tI

2

m

(2.23)

(2.24)

(2.25)

or thin walled rectangular hollow sections, eq. (2.22)

(2.26)

he first term in eq. (2.23) is generally only used for

he exact, more complicated equations for the cross

.3.6 Internal pressure

he design capacity per unit length, shown in Fig.

4r2bh2 mmmA

4rhbA 2mmmm

Fcan be approximated by:

tbh2W mmt

Topen sections. However, research by Marshall (1971)showed that the given formula provides the best fitwith the test results.

Tsectional properties are given in EN 10210-2 (2006)and EN 10219-2 (2006).

2

he circular hollow section is most suitable to resistTan internal pressure p.

T

2.11, is given by:

t2d

t2fp yd

(2.27)

M0

ectional classification,

.4 DRAG COEFFICIENTS

hollow sections,

.5 CORROSION PROTECTION

tructures designed in hollow sections have a 20 to

eq. (2.27), = 1,0, but for transport pipelines, theInM0 value may be considerably larger than for othercases, depending on the hazard of the product, theeffect of failure on the environment and inspectability.The design capacities for RHS sections subjected tointernal pressure are much more complicated;reference can be made to the DeutscherDampfkesselausschu (1975).

2.3.7 Combined loadings

arious combinations of loadings are possible, e.g.Vtension, compression, bending, shear and torsion.

Depending on the cross svarious interaction formulae should be applied.Reference can be made to Eurocode 3 (EN 1993-1-1).It is beyond the scope of this book to deal with allpossible formulae; however, the interaction betweenthe various loads in the cross section can be based onthe Huber-Hencky-Von Mises stress criterion (Roik &Wagenknecht, 1977). For the member checks, otherinteraction formulae apply, see e.g. EN1993-1-1.

2

ially circularHollow sections, espechave a striking advantage for use in structuresexposed to fluid currents, i.e. air or water. The dragcoefficients are much lower than those of opensections with sharp edges, see Fig. 2.12 (Schulz,1970; CIDECT, 1984; Dutta, 2002).

2

tructures made of hollow sections offer advantagesSwith regard to corrosion protection. Hollow sectionshave rounded corners (Fig. 2.13) resulting in a betterprotection than that for sections with sharp corners.This is especially true for the joints in circular hollowsections where there is a smooth transition from onesection to another. This better protection increasesthe protection period of coatings against corrosion.

S

50% smaller surface to be protected than comparablestructures made of open sections. Many

14


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investigations, summarized by Tissier (1978), havebeen conducted to assess the likelihood of internalcorrosion. These investigations, carried out in variouscountries, show that internal corrosion does not occurin sealed hollow sections.

Even in hollow sections which are not perfectly

.6 USE OF INTERNAL VOID

he possibilities of using the internal space are briefly

.6.1 Concrete filling

wall thicknesses are not

very important reason for using concrete filled

oncrete filling of hollow sections contributes not only

.6.2 Fire protection by water circulation

nother method for fire protection of buildings is to

he columns are interconnected with a water storage

order to prevent freezing, potassium carbonate

.6.3 Heating and ventilation

he inner voids of hollow sections are sometimes

.6.4 Other possibilities

ometimes hollow section chords of lattice girder

.7 AESTHETICS

rational use of hollow sections leads in general to

sealed, internal corrosion is limited. If there is concernabout condensation in an imperfectly sealed hollowsection, a drainage hole can be made at a point wherewater can drain by gravity.

2

he internal void in hollow sections can be used inTvarious ways, e.g. to increase the compressiveresistance by filling with concrete, or to provide fireprotection. In addition, heating or ventilation systemsare sometimes incorporated into hollow sectioncolumns.

Tdescribed below.

2

the commonly-availableIfsufficient to meet the required load bearing resistance,the hollow section can be filled with concrete. Forexample, it may be preferable in buildings to have thesame external dimensions for the columns on everyfloor. At the top floor, the smallest wall thickness canbe chosen, and the wall thickness can be increasedwith increasing load for lower floors. If the hollowsection with the largest available wall thickness is notsufficient for the ground floor, the hollow section canbe filled with concrete to increase the load bearingresistance.

Ahollow sections is that the columns can be relativelyslender. Design rules are given in e.g. Eurocode 4(EN 1994-1-1, 2004).

Cto an increase in load bearing resistance, but it alsoimproves the fire resistance duration. Extensive testprojects carried out by CIDECT and the EuropeanCoal and Steel Community (ECSC) showed thatreinforced concrete filled hollow section columnswithout any external fire protection like plaster,

vermiculite panels or intumescent paint, can attain afire life of even 2 hours depending on the cross

section ratio of the steel and concrete, reinforcementpercentage of the concrete and the applied load, seeFig. 2.14 (Twilt et al., 1994).

2Ause water filled hollow section columns.

Ttank. Under fire conditions, the water circulates byconvection, keeping the steel temperature below thecritical value of 450 C. This system has economicaladvantages when applied to buildings with more thanabout 8 storeys. If the water flow is adequate, theresulting fire resistance time is virtually unlimited.

In(K2CO3) is added to the water. Potassium nitrate isused as an inhibitor against corrosion.

2Tused for air and water circulation for heating andventilation of buildings. Many examples in offices andschools show the excellent combination of the

strength function of hollow section columns with theintegration of heating or ventilation systems. Thissystem offers maximization of floor area throughelimination of heat exchangers, a uniform provision ofwarmth and a combined protection against fire.

2Sbridges are used for conveying fluids (pipe bridge). Inbuildings, the rain water downpipes may go through

the hollow section columns or in other cases electricalwiring is located in the columns. The internal spacecan also be used for prestressing a hollow section.

2Astructures which are cleaner and more spacious.Hollow sections can provide slender aestheticcolumns, with variable section properties but flushexternal dimensions. Due to their torsional rigidity,

hollow sections have specific advantages in foldedstructures, V-type girders, etc.

15


24/240

16

often made of hollowsections directly connected to one another without anystiffener or gusset plate, is often preferred byarchitects for structures with visible steel elements.However, it is difficult to express aesthetic features ineconomic comparisons. Sometimes hollow sections

are used only because of aesthetic appeal, see e.g.Fig. 2.15, whilst at other times appearance is lessimportant.

Lattice construction, which is


25/240

Table 2.1a Hot finished structural hollow sections Non-alloy steel properties (EN 10210-1, 2006)

Minimum yield strength (1)(N/mm2)

Minimum tensilestrength(N/mm2)

Longitudinal (2)minimum elongation (%)

on gauge

oo S65,5L

Charpy impactstrength

(10 x 10 mm)Steeldesignation

t 16mm

16 < t 40mm

40< t 63mm

t < 3mm

3 t 100mm

3 < t 40mm

40 < t 63mm

Temp.C

J

S235JRH 235 225 215 360-510 360-510 26 25 20 27

S275J0HS275J2H

275 265 255 430-580 410-560 23 220

-202727

S355J0HS355J2HS355K2H

355 345 335 510-680 470-630 22 210

-20-20

272740 (3)

(1) For thicknesses above 63 mm, these values are further reduced.(2) In transverse direction 2% lower.(3) Corresponds to 27 J at -30 C.

Table 2.1b Cold formed welded structural hollow sections Non-alloy steel (EN 10219-1, 2006) Steel

propertiesdifferent from EN 10210-1 (2006)

Steel designationMinimum longitudinal elongation (%),

all thicknesses, tmax = 40 mm

S235JRH 24 (1)

S275J0HS275J2H

20 (2)

S355J0HS355J2HS355K2H

20 (2)

(1) For t > 3 mm and d/t < 15 or 5,12t2

hb

the minimum elongation is reduced by 2 to 22%; for t 3 mm the minimum

elongation is 17%.

(2) For d/t < 15 or 5,12t2

hb

the minimum elongation is reduced by 2 to 18%.

17


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Table 2.2a Hot finished structural hollow sections Fine grain steel properties (EN 10210-1, 2006)

Minimum yield strength(N/mm2)

Minimumtensile strength

(N/mm2)

Minimum elongation (%)on gauge

oo S65,5L

t 65 mm

Charpy impactstrength

(10 x 10 mm)Steeldesignation

t 16mm

16 < t 40mm

40 < t 65mm

t 65mm

Long. Trans.Temp.C

J

S275NHS275NLH

275 265 255 370-510 24 22-20-50

40 (1)27

S355NHS355NLH

355 345 335 470-630 22 20-20-50

40 (1)27

S420NHS420NLH

420 400 390 520-680 19 17-20-50

40 (1)27

S460NHS460NLH

460 440 430 540-720 17 15-20-50

40 (1)27

(1) Corresponds to 27 J at -30 C.

Table 2.2b Cold formed welded structural hollow sections Fine grain steel (EN 10219-1, 2006) Steel

properties different from EN 10210-1 (2006)

Feed stock condition M (1)

Steel designationMinimum tensile strength

(N/mm2)Minimum longitudinal

elongation (%) (2)

S275MHS275MLH

360 - 510 24

S355MHS355MLH

450 - 610 22

S420NHS420NLH

520 - 660 19

S460NHS460NLH

530 - 720 17

(1) M refers to thermal mechanical rolled steels.

(2) For d/t < 15 or 5,12t2

hb

the minimum elongation is reduced by 2, e.g. from 24% to 22% for S275MH and S275MLH.

Table 2.3 Minimum inner corner radii of cold formed RHS according to EN 1993-1-8 (2005)

Maximum wall thickness t (mm)

Generalr/tStrain due to cold

forming (%)Predominantly static

loadingFatigue dominating

Aluminium-killed steel(Al 0,02%)

25 10

3,0

2,0

1,5 1,0

2 5 14

20

25 33

anyany2412

84

any161210

84

anyany2412

106

18


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Table 2.4a Hot finished structural hollow sections Tolerances (EN 10210-2, 2006)

Section type Square/rectangular Circular

Outside dimension the greater of 0,5 mm and 1% (1)the greater of 0,5 mm and 1% but notmore than 10 mm

Welded -10%

Thickness Seamless -10% and -12,5% at maximum 25% cross section

Welded 6% on individual lengthsMass

Seamless -6%; +8%

Straightness 0,2% of the total length and 3 mm over any 1 m length

Length (exact) +10 mm, -0 mm, but only for exact lengths of 2000 to 6000 mm

Out of roundness - 2% for d/t 100

Squareness of sides 90 1 -

Corner radii Outside 3,0t maximum -

Concavity/convexity 1% of the side -

Twist 2 mm + 0,5 mm/m (1) -(1) For elliptical hollow sections with h 250 mm, the tolerances are twice the values given in this table.

Table 2.4b Cold formed welded structural hollow sections (EN 10219-2, 2006) Tolerances different

from EN 10210-2 (2006)

Section type Square/rectangular Circular

Outside dimensionb < 100 mm: the greater of 0,5 mm and 1%100 mm h, b 200 mm: 0,8%b > 200 mm: 0,6%

1%, minimum 0,5 mmmaximum 10 mm

Thickness Welded t 5 mm: 10%t > 5 mm: 0,5 mm

for d 406,4 mm:

t 5 mm: 10%t > 5 mm: 0,5 mm

for d > 406,4 mm: 10% with maximum 2,0 mm

Mass 6% 6%

Straightness0,15% of the total length and 3 mm over any 1 mlength

Outside corner radii(profile)

t 6 mm: 1,6 to 2,4t6 mm < t 10 mm: 2,0 to 3,0tt > 10 mm: 2,4 to 3,6t

-

Concavity/convexity maximum 0,8% with a minimum of 0,5 mm -

Table 2.5 Special shapes available

Triangular Hexagonal Octagonal Flat - oval Elliptical Half-elliptical

Shape

19


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Table 2.6 European buckling curves according to manufacturing processes (EN 1993-1-1, 2005)

Cross section Manufacturing process Buckling curves

Hot finished420 N/mm2 < fy 460 N/mm

2 a0

Hot finishedfy 420 N/mm

2a

Cold formed c

h

b

Flange

Webt

h

b

Flange

Webh

b

h

b

Flange

Webt

h

b

Flange

Webt

h

b

Flange

Webh

b

h

b

Flange

Webt

b

tdt dt d

th

b

Flange

Webt

h

b

Flange

Webh

b

h

b

Flange

Webt

h

b

Flange

Webt

h

b

Flange

Webh

b

h

b

Flange

Webt

b

tdt dt d

thh

Table 2.7 Limits for b/t, h/t and d/t for cross section classes 1, 2 and 3 (EN 1993-1-1, 2005)

Class 1 2 3

fyd (N/mm2) fyd (N/mm

2) fyd (N/mm2)

Crosssection

Load type Consideredelement

235 275 355 460 235 275 355 460 235 275 355 460

3f

235c

t

b

yd

c = 33 c = 38 c = 42

RHSb/t (1)

Compression Top face

36,0 33,5 29,8 26,6 41,0 38,1 33,9 30,2 45,0 41,8 37,2 33,0

3f

235c

t

h

yd

c = 72 c = 83 c = 124

RHSh/t (1)

Bending Side wall (2)

75,0 69,6 61,6 51,8 86,0 79,7 70,5 62,3 127,0 117,6 103,9 91,6

ydf

235c

t

d

c = 50 c = 70 c = 90

CHSd/t

Compressionand/orbending

t tt t

50,0 42,7 33,1 25,5 70,0 59,8 46,3 35,8 90,0 76,9 59,6 46,0

(1) For all hot finished and cold formed RHS, it is conservative to assume that the width-to-thickness ratio of the "flat" is

3t

b

t

2r-2t-b or 3

t

h

t

2r-2t-h .

(2) Wilkinson & Hancock (1998) suggested reducing the Eurocode limits (EN 1993-1-1) for the side wall slenderness of RHS

considerably, e.g. for class 1 in a simplified form to:t

b83,077

t

h with 34

t

b .

20


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Table 2.8 Allowable span-to-depth ratios L/(h-t) to avoid lateral buckling based on EN 1993-1-1 (2005)

th

L

th

tb

S235 S275 S355 S460

0,5 73,7 63,0 48,8 37,7

0,6 93,1 79,5 61,6 47,5

0,7 112,5 96,2 74,5 57,5

0,8 132,0 112,8 87,4 67,4

0,9 151,3 129,3 100,2 77,3

1,0 170,6 145,8 112,9 87,2

h

b

lange

t

h

b

lange

h

b

h

b

lange

t

h

b

lange

t

h

b

lange

h

b

h

b

lange

t

b

ht

h

b

lange

t

h

b

lange

h

b

h

b

lange

t

h

b

lange

t

h

b

lange

h

b

h

b

lange

t

b

ht

Table 2.9 Torsional strength of various sections

SectionMass(kg/m)

Torsion constant It(104 mm4) or (cm4)

UPN 200 25,3 11,9

INP 200 26,2 13,5

HEB 120 26,7 13,8

HEA 140 24,7 8,1

140 x 140 x 6 24,9 1475

168.3 x 6 24,0 2017

21


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Fig. 2.1 Lamellar tearing

Actual fy mean

after cold forming

Actual fy mean

after cold forming

Actual fy mean

after cold forming

Fig. 2.2 Influence of cold forming on the yield strength for a square hollow section of 100 x 100 x 4 mm

0

1,00

0,75

0,50

0,25

00 0,5 1,0 1,5 2,0

00

1,00

0,75

0,50

0,25

00 0,5 1,0 1,5 2,0

Fig. 2.3 Eurocode 3 buckling curves (EN 1993-1-1, 2005)

22


31/240

Buc

klings

tress

(N/mm

2)

Buc

klings

tress

(N/mm

2)

Fig. 2.4 Comparison of the masses of hollow and open sections under compression in relation to the loading

Fig. 2.5 Restraints for the buckling of a brace member

Fig. 2.6 Bottom chord laterally spring supported by the stiffness of the members, joints and purlins

23


32/240

Mpl

Mel

Me

Mpl

Mel

Me

Fig. 2.7 Moment-rotation curves Fig. 2.8 Stress distribution for bending

Fig. 2.9 Moment distribution in relation to the cross section classification

24


33/240

Fig. 2.10 Elastic shear stress distribution

tfydt fyd t fyd

t

d - 2t

Fig. 2.11 Internal pressure

Fig. 2.12 Wind flow for open and circular hollow sections

25


34/240

paint layers

steelsteel

corner protection for RHS

and open sections

paint layers

steelsteel


and open sections

paint layers

steelsteel


and open sections

paint layers

steelsteel


and open sections

Fig. 2.13 Painted corners of RHS vs. open sections

Fig. 2.14 Fire resistance of concrete filled hollow sections

RHS 304,8x304,8x9,5

111 min.

14 min.

only

RHS

non-

reinforced

concrete

filling

50min.

steel fibre

reinforced

concrete

filling

working load (kN)

firelife(min.)

1650. 3150. 3150.

120.

60.

RHS 304,8x304,8x9,5

111 min.

14 min.

only

RHS

non-

reinforced

concrete

filling

50min.

steel fibre

reinforced

concrete

filling

working load (kN)

firelife(min.)

1650. 3150. 3150.

120.

60.

RHS 304,8x304,8x9,5

111 min.

14 min.

only

RHS

non-

reinforced

concrete

filling

50min.

steel fibre

reinforced

concrete

filling

working load (kN)

firelife(min.)

1650. 3150. 3150.

120.

60.

26


35/240

Fig. 2.15 Aesthetically appealing structures

27


36/240

28


37/240

3. APPLICATIONS

The applications of structural hollow sections nearlycover all fields. Hollow sections may be used becauseof the beauty of their shape or to express lightness,

while in other cases their geometrical propertiesdetermine their application. In this chapter, examplesare given for the various fields and to show thepossibilities of constructing with hollow sections.

3.1 BUILDINGS AND HALLS

In buildings and halls, hollow sections are mainly usedfor columns and lattice girders or space frames forroofs. In modern architecture, they are also used forother structural or architectural reasons, e.g. facades.

Fig. 3.1 shows a 10-storey building in Karlsruhe,Germany with rectangular hollow section columns180 x 100. Special aspects are that the columns aremade of weathering steel and are water filled toensure the required fire protection. The columns areconnected with water reservoirs to ensure circulation.Besides the fire protection, a further advantage is thatdue to the water circulation in the columns, thedeformation of the building due to temperaturedifferences by sunshine is limited.

Fig. 3.2 shows an example of lattice girder trussesused in a roof of an industrial building. For an optimalcost effective design, it is essential that the truss jointsare made without any stiffening plates.

An especially appealing application is given in Fig.3.3, showing a tree-type support of the airportdeparture hall in Stuttgart, Germany. For the joints,streamlined steel castings are used.

Fig. 3.4 shows the roof of the terminal of KansaiInternational Airport in Osaka, Japan with curved

triangular girders of circular hollow sections.

Fig. 3.5 shows a dome under construction, whereasFig. 3.6 illustrates a special application using columnsand beams in the faade for ventilation assuring cleanwindows in the swimming pool.

Fig. 3.7 shows a very nice architectural application inBush Lane House in the city of London, UK. Theexternal circular hollow section lattice transfers thefaade loads and the loads on the floors to the maincolumns. The hollow sections are filled with water forfire protection.

Very attractive applications can be found in the hallsand buildings for the Olympic Games in Athens, e.g.Fig. 3.8.

Elliptical hollow sections are becoming more andmore popular among architects and already several

examples exist, see for example Fig. 3.9, the airportbuilding in Madrid.

Nowadays, many examples of tubular structures arefound in railway stations (Figs. 3.10 and 3.11) androofs of stadia and halls (Figs. 3.12 to 3.14).

Indeed, as stated by one of the former CIDECT vicepresidents, Jim Cran, at the Tubular StructuresSymposium in Delft (1977) "The sky is the limit", whilstpresenting beautiful applications of structural hollowsections.

3.2 BRIDGES

As mentioned in the introduction, the Firth of ForthBridge is an excellent example of using the hollowsection shape for structural applications in bridges.Nowadays, many modern examples exist (IISI, 1997).Figs. 1.4, 3.15 to 3.17 and 3.20 show variousexamples of pedestrian bridges; some of these aremovable bridges.

Circular hollow sections can also be used as a flangefor plate girders, as shown in Fig. 3.17 for a triangularbox girder.

A very nice example of a road-pedestrian bridge isillustrated in Fig. 3.18, being a compositesteel-concrete bridge with hollow sections for the archand braces and a concrete deck.

Fig. 3.19 shows a railway bridge near Rotterdam, TheNetherlands with circular hollow section arches.

3.3 BARRIERS

There are a few aspects which make hollow sectionsincreasingly suitable for hydraulic structures, such asbarriers. Due to environmental restrictions, themaintenance of hydraulic structures requires severeprecautions, making durability an important issue.Structures of hollow sections are less susceptible tocorrosion due to the rounded corners. Furthermore,especially circular hollow sections have lower drag

coefficients, leading to lower forces due to waveloading. Fig. 3.21 shows a barrier with a support

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structure of circular hollow sections. Fig. 3.22 showsthe storm surge barrier near Hook of Holland withtriangular arms made of circular hollow sections and alength (250 m) equal to the height of the Eiffel Towerin Paris.

3.4 OFFSHORE STRUCTURES

Offshore, many application examples are available;most of them in circular hollow sections. For thesupport structure, the jacket or tower, not only is thewave loading important, but also other aspects areleading to the use of circular hollow sections. E.g. in jackets, the circular hollow section piles are oftendriven through the circular hollow section legs of the jacket, thus the pile is guided through the leg.Sometimes the internal void is used for buoyancy.Further, the durability and easy maintenance insevere environments are extremely important.

Hollow section members are used in jackets, towers,the legs and diagonals in topside structures, cranes,microwave towers, flare supports, bridges, supportstructures of helicopter decks and further in varioussecondary structures, such as staircases, ladders, etc.Figs. 3.23 and 3.24 show two examples.

3.5 TOWERS AND MASTS

Considering wind loading, corrosion protection andarchitectural appearance, there is no doubt that hollowsections are to be preferred. However, in manycountries, electric power transmission towers aremade of angle sections with simple bolted joints.

Nowadays, architectural appearance becomes moreimportant, while stringent environmental restrictionsmake protection and maintenance increasinglyexpensive. These factors stimulate designs made of

hollow sections (Figs. 3.25 and 3.26).

3.6 SPECIAL APPLICATIONS

The field of special applications is large, e.g. along theroads, petrol stations (Fig. 3.27), sound barriers (Fig.3.28), traffic information gantries (Fig. 3.29), guardrails, parapets and sign posts.

Further, excellent application examples are found inradio telescopes (Fig. 3.30), in mechanical

engineering, cranes (Fig. 3.31) and roller coasters(Fig. 3.32).

In the agricultural field, glass houses (Fig. 3.33) andagricultural machinery are typical examples. Also intransport, many examples exist but these are outsidethe scope of this book. Indeed, the sky is the limit.

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Fig. 3.2 Roof with lattice girders

Fig. 3.1 Faade of the Institute for Environment inKarlsruhe, Germany

Fig. 3.3 Airport departure hall in Stuttgart, Germany

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Fig. 3.4 Roof of Kansai International Airport in Osaka,

Japan

Fig. 3.6 Faade with ventilation through the RHScolumns and beams, Borkum, Germany

Fig. 3.8 Hall for the 2004 Olympic Games, Athens,Greece

Fig. 3.5 Dome structure in Gothenburg, Sweden

Fig. 3.7 Bush Lane House in London, UK

Fig. 3.9 Airport Madrid with EHS sections, Spain

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Fig. 3.10 Railway station in Rotterdam, TheNetherlands

Fig. 3.12 Barrel dome grid for the Trade Fair buildingin Leipzig, Germany

Fig. 3.13 Retractable roof for the Rogers Centre inToronto, Canada

Fig. 3.11 TGV railway station at Charles de GaulleAirport, France

Fig. 3.14 Stadium Australia for the 2000 OlympicGames, Sydney, Australia

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Fig. 3.15 Movable pedestrian bridge in RHS, TheNetherlands

Fig. 3.17 Pedestrian bridge in Houdan, France

Fig. 3.19 Railway bridge with CHS arches, TheNetherlands

Fig. 3.21 Eastern Scheldt barrier, The Netherlands

Fig. 3.16 Movable pedestrian bridge in RHS nearDelft, The Netherlands

Fig. 3.18 Composite road bridge in Marvejols, France

Fig. 3.20 Movable pedestrian bridge in CHS nearDelft, The Netherlands

Fig. 3.22 Storm surge barrier, The Netherlands

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Fig. 3.23 Bullwinkle offshore structure, Gulf of Mexico

Fig. 3.25 Electric power transmission tower

Fig. 3.27 Petrol station, The Netherlands

Fig. 3.24 Amoco P15 offshore platform with jack-up,North Sea

Fig. 3.26 Mast, The Netherlands

Fig. 3.28 Sound barrier, Delft, The Netherlands

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Fig. 3.29 Traffic information gantry, The Netherlands

Fig. 3.30 Radio telescope

Fig. 3.31 Cranes

Fig. 3.33 Green house, The Netherlands Fig. 3.32 Roller coaster

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4. COMPOSITE STRUCTURES

4.1 INTRODUCTION

Concrete filled hollow sections (Fig. 4.1) are mainly

used for columns. The concrete filling gives a higherload bearing capacity without increasing the outerdimensions. The fire resistance can be considerablyincreased by concrete filling, in particular if properreinforcement is used.

Due to the fact that the steel structure is visible, itallows a slender, architecturally-appealing design. Thehollow section acts not only as the formwork for theconcrete, but also ensures that the assembly anderection in the building process are not delayed by thehardening process of the concrete.

CIDECT research on composite columns startedalready in the sixties, resulting in monographs anddesign rules, adopted by Eurocode 4 (EN 1994-1-1,2004). CIDECT Design Guide No. 5 (Bergmann et al.,1995) provides detailed information for the staticdesign of concrete filled columns.

To a large extent, this chapter follows the informationgiven in Design Guide No. 5, but updated with thelatest revisions to Eurocode 4 (EN 1994-1-1).

4.2 DESIGN METHODS

In the last decades, several design methods forcomposite columns were developed, e.g. in Europe byGuiaux & Janss (1970), Roik et al. (1975) and Virdi &Dowling (1976), finally resulting in the design rulesgiven in Eurocode 4 (EN 1994-1-1, 2004).

In this chapter, the design method given is based onthe approach presented in Eurocode 4 (EN 1994-1-1).The design of composite columns has to be carried

out at the ultimate limit state, i.e. the effect of the mostunfavourable combination of actions should notexceed the resistance of the composite member.

An exact calculation of the load bearing capacityconsidering the effect of imperfections and deflections(second order analysis), the effect of plastification ofthe section, cracking of the concrete, etc. can only becarried out by means of a computer program. Withsuch a program, the resistance interaction curves asshown in Fig. 4.2, can be calculated. Based on thesecalculated capacities, the following simplified designmethods have been developed.

4.3 AXIALLY LOADED COLUMNS

From the work of Roik et al. (1975), a simplifieddesign method is given in Eurocode 4 (EN 1994-1-1),similar to the design method adopted for steelcolumns, i.e.:

Rd,plEd NN (4.1)

where:NEd design normal force (including load factors) reduction factor for the relevant buckling curve,

i.e. curve "a" fors 3% andcurve "b" for 3% < s 6% (see Fig. 2.3)

Npl,Rd resistance of the cross section to normal forceaccording to eq. (4.2)

Npl,Rd = Aa fyd + Ac fcd + As fsd (4.2)

where:Aa, Ac, As cross sectional areas of structural steel,

concrete and reinforcementfyd, fcd, fsd design strengths of steel, concrete (see

Table 4.1) and reinforcement using therecommended M factors according toEurocode 2 (EN 1992-1-1, 2004) andEurocode 3 (EN 1993-1-1, 2005) being a =1,0 for fy, c = 1,5 for fc, and s = 1,15 for fs

The load factors for the actions F have to bedetermined from EN 1990 (2002).

Concrete classes higher than C50/60 should not beused without further investigation and classes lowerthan C20/25 are not allowed for compositeconstruction.

In concrete filled hollow sections, the concrete isconfined by the hollow section. Therefore, theconcrete strength reduction factor of 0,85 does not

have to be considered.

The reduction factor follows from the relative

slenderness

eff,cr

Rk,pl

E N

N

(4.3)

where:Npl,Rk resistance of the cross section to axial load

according to eq. (4.2), however, with fyd, fcd and

fsd replaced by fyk, fck and fskNcr,eff elastic buckling capacity of the member (Euler

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critical load)

Ncr,eff= 2b

eff)EI(

(4.4)

where:b buckling length of the column(EI)eff effective stiffness of the composite section

The buckling (effective) length of the column can bedetermined by following the rules of Eurocode 3 (EN1993-1-1).

(EI)eff= Ea Ia + 0,6 Ec,effIc + Es Is (4.5)

Ec,eff=

tEd

Ed,G

cm

N

N

1

E

(4.6)

where:Ia, Ic, Is moments of inertia of the cross sectional

areas of structural steel, concrete (with thearea in tension assumed to be uncracked)and reinforcement, respectively

Ea, Ecm, Es moduli of elasticity of structural steel,concrete and reinforcement

Ec,eff modulus of elasticity of concrete correctedfor creep with Ecm according to Table 4.1

NEd acting design normal forceNG,Ed permanent part of NEdt creep factor according to Clause 3.1 of

Eurocode 2 (EN 1992-1-1)

The calibration factor 0,6 in eq. (4.5) is incorporated toconsider, for example, the effect of cracking ofconcrete under moment action due to second ordereffects.

4.3.1 Limitations

The reinforcement to be included in the designcalculations should not exceed 6% of the concretearea. There is no minimum requirement.

The composite column is considered as "composite"if:

0,2 0,9 (4.7)

where:

Rd,pl

yda

N

fA (4.8)

If the parameter is less than 0,2, the column shall bedesigned as a concrete column following Eurocode 2

(EN 1992-1-1). On the other hand, when exceeds0,9, the column shall be designed as a steel columnaccording to Eurocode 3 (EN 1993-1-1).

To avoid local buckling, the following limits should beobserved for bending and compression loading (EN1994-1-1, 2004):- For concrete filled rectangular hollow sections (with

h being the greater overall dimension of thesection):

h/t 52 (4.9)

- For concrete filled circular hollow sections:

d/t 902 (4.10)

The factor accounts for different yield strengths:

=ydf

235(4.11)

with fyd in N/mm2.

Although the d/t and h/t values given in Table 4.2 areequal (for CHS) or higher (for RHS) than those ofclass 3 for unfilled sections, the plastic resistance ofthe section can be used. However, for the analysis ofthe internal forces in a structure, an elastic analysisshould be performed. Further discussions onslenderness limits for unfilled CHS and RHS and theeffect of concrete filling can be found in Zhao et al.(2005).

4.3.2 Effect of long term loading

The influence of the long-term behaviour of theconcrete on the load bearing capacity of the column isincluded by a modification of the concrete modulus ofelasticity, since the load bearing capacity of thecolumns may be reduced by creep and shrinkage. Asshown in eq. (4.6) for a load which is fully permanent,the modulus of elasticity of the concrete will beconsiderably reduced.

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4.3.3 Effect of confinement

For concrete filled circular hollow section columns with

a small relative slenderness 0,5 (for CHS, this isapproximately /d 12) and e/d 0,1, the bearing

capacity is increased due to the impeded transversestrains. This results in radial compression in theconcrete and a higher resistance to normal stresses,see Fig. 4.3. Above these values, the confinementeffect is very small.

For concrete filled rectangular hollow sections, anyconfinement effect is neglected.

Detailed information can be found in Eurocode 4 (EN1994-1-1).

4.4 RESISTANCE OF A SECTION TOBENDING

For the determination of the resistance of a concretefilled section to bending moments, a full plastic stressdistribution in the section is assumed (Fig. 4.4). Theconcrete in the tension zone of the section is assumedto be cracked and is therefore neglected. The internalbending moment resulting from the stresses anddepending on the position of the neutral axis is theresistance of the section to bending moments Mpl,Rd.

4.5 RESISTANCE OF A SECTION TOBENDING AND COMPRESSION

The resistance of a concrete filled cross section tobending and compression can be shown by theinteraction curve between the normal force and theinternal bending moment.

Figs. 4.5 to 4.8 show the interaction curves for RHS

and CHS columns in relation to the cross sectionparameter . These curves have been determinedwithout any reinforcement, but they may also be usedfor reinforced sections if the reinforcement isconsidered in the values and in Npl,Rd and Mpl,Rdrespectively.

The interaction curve has some significant points,shown in Fig. 4.9. These points represent the stressdistributions given in Fig. 4.10. The internal momentsand axial loads belonging to these stress distributionscan be easily calculated if effects of the corner radius

are excluded.

Comparing the stress distribution of point B, where thenormal force is zero, and that of point C with the samemoment as in point B and axial force NC,Rd (Fig. 4.10),the neutral axis moves over a distance 2hn. Hence,the normal force NC,Rd can be calculated by theadditional compressed parts of the section with depth

2hn. Because the force NC,Rd does not contribute tothe moment MC,Rd = MB,Rd.

Furthermore, the normal force at point C is twice thevalue of that at point D: NC,Rd = 2ND,Rd.

4.6 INFLUENCE OF SHEAR FORCES

The influence of the shear stresses on the normalstresses does not need to be considered if:

VEd 0,5Vpl,Rd (4.12)

The shear force on a composite column may either beassigned to the steel profile alone or be divided into asteel and a reinforced concrete component. Thecomponent for the structural steel can be consideredby reducing the axial stresses in those parts of thesteel profile which are effective for shear (Fig. 4.11).

The reduction of the axial stresses due to shearstresses may be carried out according to the

Huber-Hencky-Von Mises criterion or according toEurocode 4 (EN 1994-1-1). For the determination ofthe cross-section interaction, it is easier to transformthe reduction of the axial stresses into a reduction ofthe relevant cross sectional areas equal to that usedfor hollow sections without concrete filling:

reduced Av = Av

2

Rd,pl

Ed 1V

V21 (4.13)

3

f

AVyd

vRd,pl (4.14)

For Av, see Chapter 2.

4.7 RESISTANCE OF A MEMBER TOBENDING AND COMPRESSION

4.7.1 Uniaxial bending and compression

Fig. 4.12 shows the principle of the method for the

design of a composite member under combinedcompression and uniaxial bending using the

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cross-section interaction curve. Due to imperfections,the resistance of an axially loaded member is given byeq. (4.1) oron the vertical axis in Fig. 4.12.

The moment capacity factor at the level of is definedas the imperfection moment. Having reached the load

bearing capacity for axial compression, the columncannot resist any additional bending moment.

The value of d resulting from the actual designnormal force NEd (d = NEd/Npl,Rd) determines themoment capacity factor d for the capacity of themember. This factor d gives the moment capacityincluding the imperfection moment, thus theimperfection moment should be added to the externalmoment including second order effects.

The capacity for the combined compression andbending of the member can now be checked by:

M||,maxMd Mpl,Rd (4.15)

where:M||,max design bending moment of the column,

including the imperfection moment and secondorder effects

M 0,9 for S235 to S335 and 0,8 for S420 andS460

d to be obtained from the interaction diagrams in

Figs. 4.5 to 4.8

The additional reduction by the factorM accounts forthe assumptions of this simplified design method, e.g.the interaction curve of the section is determinedassuming full plastic behaviour of the materials withno strain limitation.

Note: Interaction curves of the composite sectionsalways show an increase in the bending capacityhigher than Mpl,Rd. The bending resistance increaseswith an increasing normal force, because former

regions in tension are compressed by the normalforce. This positive effect may only be taken intoaccount if it is ensured that the bending moment andthe axial force always act together. If this is notensured, and the bending moment and the axial forceresult from different loading situations, the relatedmoment capacity d has to be limited to 1,0.

Columns with equal end moments

The verification procedure for columns with the sameend moments given in Eurocode 4 (EN 1994-1-1) isas follows:

The second order moment MEd,|| can be approximated

by:

MEd,|| = k MEd (4.16)

where:

eff,cr

Ed

N

N1

1k

(4.17)

k is the amplification factor to incorporate the secondorder effects.

Ncr,eff can be determined with eq. (4.4), however, witha modified (EI)eff,|| due to the simplifications mentionedbefore:

(EI)eff,|| = 0,9 (Ea Ia + 0,5 Ec,effIc + Es Is) (4.18)

The total moment including the imperfection momentis:

M||,max =

eff,cr

Ed

N

N1

1

(MEd + NEd e0) (4.19)

The capacity can now be checked with eq. (4.15).

Columns with different end momentsIf the end moments are not equal (see Fig. 4.13), thenthe k factor in eq. (4.17) has to be corrected for theexternal moment by a factor:

eff,cr

Ed

N

N1

k

(4.20)

where:

= 0,66 + 0,44r but 0,44 (4.21)

with r being the ratio between the smallest and largestend moment (Fig. 4.13).

The total moment including the imperfection momentis now:

eff,cr

Ed

0Ed

eff,cr

Ed

Edmax||,

N

N1

eN

N

N1

MM

(4.22)

This moment has to be used in eq. (4.15). If the firstorder moment is larger than MEd,||, then this value

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should be used. 4.9 SPECIAL COMPOSITE MEMBERSWITH HOLLOW SECTIONS

4.7.2 Biaxial bending and compression The previous sections consider composite membersconsisting of a hollow section at the outer side and

concrete inside. The concrete may be reinforced ornot. However, an alternative is to reinforce theconcrete with steel fibres instead of reinforcing barswhich provide advantages in the extension of the fireresistance.

A composite member under biaxial bending and

compression has first to be examined for both axesunder uniaxial bending and compression, see Section4.7.1. Additionally the combined situation has to beverified. The influence of the imperfection is onlytaken into account for the buckling axis which is mostcritical.

41

The check can be expressed by the followingcondition:

0,1

M

M

M

M

Rd,z,pldz

Ed,z

Rd,y,pldy

Ed,y

(4.23)

Other types of reinforcement used are solid sectionsor another hollow section inside a circular orrectangular hollow section with concrete in between.Fig. 4.16 shows an example of a CHS with anotherCHS member inside. Although many combinations arepossible, the design is in principle similar to that for

the reinforced concrete hollow section columnsdescribed in the previous sections (Zhao et al., 2010).

The values dy and dz are determined at the level ofd.

4.8 LOAD INTRODUCTION

In the design of composite columns, a full compositeaction of the cross section is assumed. This meansthat in the bond area no significant slip can occurbetween the steel and the concrete. At locations of

load introduction, e.g. at beam-column connections,this has to be verified. If no calculation is carried out,the length of load introduction should be assumed tobe the minimum of 2b, 2d or/3, where b or d is theminimum transverse dimension of the column, and is the column length.

If the steel is not painted and is free of oil and rust, themaximum bond stress, based on friction is (EN1994-1-1, 2004):- Rd = 0,55 N/mm

2 for CHS columns- Rd = 0,40 N/mm

2 for RHS columns

The shear load transfer can be increasedconsiderably by shear connectors or steelcomponents, see Fig. 4.14.

For concentrated loads, a load distribution accordingto Fig. 4.15 can be assumed. For such locally loadedparts of encased concrete, higher desig

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Hollow Sections in Structural Applications 2nd Edition